This paper considers the application of conceptual mathematics to construct a computational model of concepts and individuals. An applicative approach is systematically applied to build a concept-as-process design. Since modern computing considers information processes as the main objects of modeling, the developed design is indeed representative of the semantic processing of information. The nature of concepts – what concepts are – and the constraints that govern the theory of concepts have been, and continue to be, the subject of debate. It is especially interesting to discuss the nature of concepts in connection with the recently established fundamental nature of information processes that are attributable to all phenomena and events occurring in the world around us. The current trend elevates information processes to forms of computing, which can also be implemented through practices, for example, in the form of programming. The deep component is computational models, one way or another expressed by means of mathematics and metamathematics. The main meta-operations used are abstraction and application. Of greatest interest is functional abstraction and application in the form of applying a function to an argument. Despite this “conceptual minimalism”, a rich theory of concepts can be developed. Using this theory, it is possible to focus further discussion not only on the nature of concepts, but also to characterize the position on each of the five important issues that are central to many theories of concepts: (1) ontology of concepts, (2) structure of concepts, (3) empiricism, and nativism about concepts, (4) concepts and natural language, and (5) concepts and conceptual analysis.
